We study suspended, 300-nm-long single-walled carbon nanotubes (SWCNT) contacted using MoRe leads. Good contact transparency of the superconductor-nanotube interface allows for the observation of proximity-induced superconductivity in our SWCNT devices. The magnitude of the switching supercurrent ranges up to 50 nA and can be tuned periodically by gate-induced charge. The gate charge modulates the retrapping current even more strongly, and its magnitude becomes vanishingly small far away from the charge degeneracy point.
Under rf irradiation, our SWCNT devices display clear Shapiro steps, the shape of which depend on the rf frequency and power. Under certain conditions the observed steps become hysteretic, indicating small dissipation on the Josephson phase dynamics at the rf frequency.
In these SWCNT devices we find mechanical resonances around 1.5 GHz, while the Q factors amount up to 15000 near the charge degeneracy point. Mechanical modes can be observed also in the superconducting regime either by mixing by the current-phase relation or by inducing Shapiro steps resonantly with the mechanical mode, which both reflect the interplay between the Josephson dynamics and the mechanical degrees of freedom. In addition, we find bifurcation of Shapiro steps around the mechanical resonance frequency, both at fundamental and subharmonic resonance drives. The understanding of these phenomena within the framework of current biased RCSJ model will be discussed.